Make the sambar masala: In a large sauté pan over low heat, toast the curry leaves, coriander, cumin, black pepper, black mustard, fenugreek seeds, poppy seeds, ground turmeric and ground cinnamon until fragrant, 2 to 3 minutes. Transfer to a small bowl and let cool. Return the pan to low heat and toast the chana dal and toor dal until lightly browned, 3 to 4 minutes. Add to the bowl of spices. Return the pan to low heat, add the oil and chiles, and cook until they brown and develop a nutty aroma, 45 seconds to 1 minute. Do not burn. Transfer to the bowl of spices and cool completely. Working in batches, finely ground the mixture in a coffee grinder or food processor. Makes ½ cup.
Make the okra sambar: Preheat the oven to 375°. Rinse the dal under cool water until the water runs clear, then drain. In a medium saucepan, combine the dal with 4 cups of the water and ½ teaspoon salt, and bring to a boil. Reduce the heat to low and cook with the lid slightly ajar at a slow, bubbling simmer until the lentils are tender and creamy, 30 to 45 minutes. Add 1 to 2 tablespoons of water if the pan looks dry.
While the dal is cooking, roast the vegetables: Separately, toss the carrots, red onions and okra each with ½ teaspoon salt and ½ teaspoon of the canola oil to lightly coat. Spread onto a parchment paper-lined baking sheet and roast until lightly browned and tender, 20 to 30 minutes. Set aside.
In a large saucepan over medium-low heat, heat the remaining 1½ teaspoons of the canola oil. Add the curry leaves, black mustard seeds, cumin, asafoetida and fenugreek, and sauté until the spices are toasted and the curry leaves are crisp, 3 to 4 minutes. Add the serrano chiles, turmeric and sambar masala, and cook until fragrant, 1 to 2 minutes. Add the remaining 4 cups of water and the roasted onions, and bring to a simmer. Add the toor dal and simmer to allow the flavors to meld, 15 to 20 minutes. Add the roasted carrots, okra, tamarind purée and crushed tomatoes, and cook another 5 to 10 minutes. Adjust the texture of soup with water if needed and adjust seasoning with salt and tamarind purée before serving.